form a binary string

Count the ways that a 100 length binary string can be formed if the times that the digit zero appears is an even number and the times that the digit one (1) appears is an even number as well. (Note: in the even numbers zero is inluded.)

Count the ways that a 100 length binary string can be formed if the times that the digit zero appears is an even number and the times that the digit one (1) appears is an even number as well. (Note: in the even numbers zero is inluded.)

Dont get it.

How many way can a binary string of length 100 be formed? (The binary string consists ONLY of 1's & 0's.)

Obviously, 64.
Maybe not so obvious is this: .
How many had an even count of 1's (or zeroes) in the string?
If you count them you will find 32.
Half of 64 (or 2^6) is 32 (or 2^5).

The FINAL EXAM!

Count the ways that a 100 length binary string can be formed if the times that the digit zero appears is an even number and the times that the digit one (1) appears is an even number as well. (Note: in the even numbers zero is inluded.)

How many ways can you have a string of 1's & 0's of length 100?
Recall:
a string length of 4 has 2^4 ways
a string length of 6 has 2^6 ways.
That should be easy.